Abstract: The present work follows numerous numerical simulation on the stress field analysis in a cracked cross-ply laminate. These results lead us to elaborate an energy criterion. This criterion is based on the computation of the partial strain energy release rate associated with all the three damage types: transverse cracking, longitudinal cracking and delamination. The related criterion, linear fracture based approach, is used to predict and describe the initiation of the different damage mechanisms. With this approach the influence of the nature of the material constituent on the damage mechanism is computed. We also give an assessment of the strain energy release rates associated with each damage mode. This criterion checked on glass-epoxy and graphite-epoxy composite materials will now be used in future research on new bio-based composite in the laboratory.